Asymptotic formulae for s-numbers of a Sobolev embedding and a Volterra type operator

TL;DR

This paper derives precise asymptotic formulas for the approximation and s-numbers of Sobolev embeddings and Volterra-type operators, enhancing understanding of their compactness properties.

Contribution

It provides sharp asymptotic estimates for s-numbers of Sobolev embeddings and Volterra operators, which were previously not well characterized.

Findings

Asymptotic formulas for approximation numbers are established.

Sharp upper and lower bounds for s-numbers are obtained.

Results improve understanding of the compactness of these operators.

Abstract

Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding and an integral operator of Volterra type. These lead to asymptotic formulae for the approximation numbers and certain other s-numbers.